Sleep is one of the fundamental requirements of all animals from nematodes to humans. It appears in different formats with shared features such as reduced muscle activities and reduced responsiveness to the environment. Despite the long history of sleep research, why a brain must be taken offline for a large portion of each day remains unknown. Moreover, sleep research focused on mammals and birds reveals two stages, rapid-eye-movement (REM) and slow-wave (SW) sleep, alternating during sleep. Whether these two stages of sleep exist in other vertebrates, particularly reptiles, is debated, as is the evolution of sleep in general. Recordings from the brain of a lizard, the Australian bearded dragon Pogona vitticeps, indicate the presence of two electrophysiological states and provides a better picture of their sleep. Local field potential (LFP) signals, head velocity, eye movements, and heart rate during sleep match the pattern of REM and SW sleep in mammals. The SW and REM sleep patterns that we observed in lizards oscillated continuously for 6 to 10 hours with a period of 80-100 seconds when the ambient temperature was ~27°C. Lizard SW dynamics closely resemble those observed in rodent hippocampal CA1, yet originated from a brain area, the dorsal ventricular ridge (DVR), that does not correspond anatomically or transcriptomically to the mammalian hippocampus. This finding pushes back the probable evolution of these dynamics to the emergence of amniotes, at least 300 million years ago. Unlike mammals and birds, REM and SW sleep in lizards occupy an almost equal amount of time during sleep. The clock-like alternation between these two sleep states was found initially by measuring the power modulation of two frequency bands, delta and beta. I recorded the full-band LFP and found an infra-slow oscillation (ISO) in the frequency range between 5 and 20 milli-Hz during sleep. The magnitude of ISO increased during sleep and decreased during both wakefulness and arousal during sleep. The up- and down-states of ISO were synchronized with the sleep state alternating rhythm but with a significant time lag dependent on the locations of the recording electrodes. Multi-site LFP recordings indicated that this ISO is a putative propagation wave sweeping extremely slowly, 30-67 µm/sec, from the posterior-dorsal pole to the anterior-ventral pole of the DVR. Previous studies in other animals showed that brainstem areas such as the locus coeruleus, laterodorsal tegmentum, and periaqueductal gray are involved in sleep states regulation. It is sadly impossible to carry out in vivo recordings in the lizard brainstem without severely affecting them and their quality of life. I thus carried out ex vivo recordings in both DVR and brainstem. Pharmacological stimulation of the brainstem could reversibly silence one distinct EEG pattern characteristic of SW sleep, the sharp-wave and ripple complex, in DVR. An ISO could be recorded simultaneously in both DVR and brainstem. From data collected in both intact and split ex vivo brains, I concluded that there are independent ISO generators in at least two areas, the brainstem and the telencephalon. Their signals may normally be synchronized by long-range connections. The DVR ISO leads the brainstem ISO by ~29 sec. Optogenetic stimulation of brainstem neurons was able to disrupt the ISO in DVR reversibly. In conclusion, the lizard brain offers a relatively simple model system to study sleep. Despite a diversity of results in different lizard species, my results revealed a number of new findings. Relevant for sleep research in general: 1) REM and SW sleep exist in a reptile. Since they also exist in birds and mammals, they probably existed in their common amniote ancestor, if not earlier. 2) REM and SW occupy equal amounts of time during sleep (50% duty cycle), a unique feature among all described sleep electrophysiological patterns, suggesting the possible existence of a simple central pattern generator of sleep, possibly ancestral. 3) I discovered the existence, in the local field potential, of an infra slow oscillation with extremely slow propagation, locked to the SW-REM alternating rhythm. The causes and mechanisms of this ISO remain to be understood. To my knowledge, the correlation between sleep states and a slow rhythm has only been reported in human scalp EEG recordings so far.